I'm feeling a bit uncertain right now about how nouns taken from Greek nouns ending in -ης are declined. According to Lewis and Short, "Arsăces, is m." is the Latin name corresponding to the Greek name Ἀρσάκης. Although L&S do not mark the e in the last syllable with a macron, I assume it is long (-ēs).

The Greek name seems to be first declension, but the Latin name is given as a third-declension noun. Similarly, the Wiktionary entry for the name Gotarzes (from Greek Γωτάρζης) marks it as a third-declension noun with the forms Gōtarzēs, Gōtarzis.

I'm confused because I expected that Greek first-declension nouns ending in -ης would be taken into Latin as first-declension nouns of the "Greek" sub-type, with nominative singular forms in -ēs and genitive singular forms in -ae (as described in Joonas's answer here).

When I do a Google search for "Arsacis" or "Gotarzis", I do get many results. I tried searching for "Gotarzae" and found an example in this document: Flavii Iosephi Antiqvitatvm Ivdaicarvm libri XX. Should this be categorized as an erroneous form? I also found results for "Arsacen" and "Gotarzen".

(I realize that names like this aren't necessarily attested in many places, so maybe there is no good way to judge which forms aside from the nominative are "correct" in Latin. If the situation is like that, an explanation of this would also count as an answer.)

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Here are all the references that I have found so far that have relevant information about the declension of nouns ending in -es that come from Greek. These references don't specifically mention Arsaces and Gotarzes.

Allen and Greenough:

Many Greek nouns vary among the 1st, the 2nd, and the 3rd declensions.

"Many names in -ēs belonging to the 3rd declension have also a genitive in -ī", giving the example "Thūcȳdidēs, Thūcȳdidī" (§52a)

Grammar of the Latin Language, by C.G. Zumpt (1836):

"the greater part of Greek nouns in ης, ου, if not patronymics, are declined after the third declension in Latin, as Alcibiades, Miltiades, Xerxes. Many of them, however, still form their accusatives in en (Euphraten, Mithridaten,) and their vocative in e" (Sect. VII.3, pp. 11-12).

"Cicero very commonly, and other authors of the best age occasionally, form from Greek nouns proper in es a genitive in i, instead of is; e.g. gr. Achilli, Ulixi (see p. 15), Isocrati, Archimedi, especially from those in cles, Agathcli, Diocli, Neocli, Procli, Pericli, Themistocli. So in the barbarian names Mithridati, Xerxi, and others." (Sect XIII, Remark 1, pp. 25-26).

"Proper names in es, genitive is, which in Greek are of the first declension, have in Latin, along with the accusative in em, the termination ēn, Achillen, Aeschinen; especially barbarous names, as Xerxen, Euphraten. This form in en is also found, though rarely, of those words which in Greek are declined after the third declension, but make ην as well as η in the accusative, e. gr. Sophoclen (Cic. Off. i. 40.), Hippocraten, Epicyden, in Livy. Words which in Greek are doubly declined, in ου and ητος, as Χρέμης, Θαλῆς, have in Latin also both forms, is and etis, and in the accusative make also en, e. gr. Chremetem, Chremem and Chremen; Thalem, Thaletem and Thalen, Ab. Thale." (Sect XIV.2, p. 32).